Mathematical Research Letters

Volume 16, Issue 2, March 2009 pp. 279-289.

The Signature of the Chern Coefficients of Local Rings

Authors: Laura Ghezzi (1), Jooyoun Hong (2), and Wolmer V. Vasconcelos (3)
Author institution: New York City College of Technology-Cuny (1), Southern Connecticut State University (2), and Rutgers University (3)

Summary: This paper considers the following conjecture: If $R$ is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal $J$ generated by a system of parameters, the Chern coefficient $e_1(J)< 0$ is equivalent to $R$ being non Cohen-Macaulay. The conjecture is established if $R$ is a homomorphic image of a Gorenstein ring, and for all universally catenary integral domains containing fields. Criteria for the detection of Cohen-Macaulayness in equi-generated graded modules are derived.

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